Toroidal effects on magnetohydrodynamic modes in tokamaks

Abstract

In order to investigate the effect of toroidal curvature on magnetohydrodynamic modes in tokamak configurations, stability criteria are derived by means of an expansion in the inverse aspect ratio. For a low-pressure system, βθ ∼ 1, with a nearly constant safety factor, q = qa(0) + …, the well known stability criterion for kink modes, relating qa to the ratio a / b of the plasma radius to that of a conducting wall, is determined in second order. Here, it is shown that toroidal effects modify this criterion favorably in fourth order when the vacuum region does not extend too far. Typically, it is found that improvement is achieved when b / a is less than 1.25 to 1.5. Interchange and ballooning effects are incorporated in the stability criteria.